Sphenic Numbers. How to identify if a number is sphenic or not spenic.

A sphenic number is a positive whole number that can be written as product of three distinct prime factors. So in order decide if a number is a sphenic number or not follow these two simple steps:

Step 1 Work out the product of prime factors for the number you are checking.

Step 2 If the product of prime factors contains 3 distinct prime factors then the number will be sphenic. If not then the number will not be sphenic.

Example 1

Is the number 42 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

42/2 = 21

21/3 = 7

So 2 × 3 × 7 = 42

Since there are 3 prime factors and all are distinct then 42 is a sphenic number.

Example 2

Is the number 18 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

18/2 = 9

9/3 = 3

So 2 × 3 × 3 = 18

18 is not a sphenic number as there are not 3 distinct prime factors.

Example 3

Is the number 78 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

78/2 = 39

39/3 = 13

So 2 × 3 × 13 = 78

Since there are 3 prime factors and all are distinct then 78 is a sphenic number.

Example 4

Is the number 210 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

210/2 = 105

105/3 = 35

35/5 = 7

So 2 × 3 × 5 × 7 = 210

210 is not a sphenic number as there are 4 distinct prime factors not 3.

Example 5

Is the number 110 a sphenic number? Explain your answer.

First work out the product of the product of prime factors:

110/2 = 55

55/5 = 11

So 2 × 5 × 11 = 110

Since there are 3 prime factors and all are distinct then 110 is a sphenic number.

More by this Author


Comments

No comments yet.

    0 of 8192 characters used
    Post Comment

    No HTML is allowed in comments, but URLs will be hyperlinked. Comments are not for promoting your articles or other sites.


    Click to Rate This Article
    working